Q7 Matemática  (IMO Shortlist 1975)

Prove que de $x+y=1(x,y\in \mathbb{R})$ segue que $$x^{m+1}\sum _{j=0}^n\left(\genfrac{}{}{0ex}{}{m+j}{j}\right)y^j+y^{n+1}\sum _{i=0}^m\left(\genfrac{}{}{0ex}{}{n+i}{i}\right)x^i=1(m,n=0,1,2,\dots ).$$